多変数関数論4

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958: １３２人目の素数さん [sage] 2025/06/04(水) 10:11:54.56 ID:Vo5laslH

https://rio2016.5ch.net/test/read.cgi/math/1745503590/432-433
＜AI Copilot さんが どれくらい賢いか？＞(そこそこ賢いようですね)

スタート
いま 数学の多変数複素関数論で 話題になっていることは 何ですか
　↓ （google英訳（を若干手直し））
What is the hot topic right now in the theory of functions of several complex variables ?

Copilotさんの回答1
One of the current hot topics in the theory of functions of several complex variables is the (L^2)-theory and its applications. Recent research has focused on the (L^2) existence theorem and (L^2) extension theorem, which play a crucial role in understanding positivity conditions in complex geometry. These results are being used to develop criteria for Griffiths positivity and Nakano positivity of Hermitian metrics on holomorphic vector bundles.
Another active area of research is the study of plurisubharmonic functions, which are essential in complex analysis and geometry. Researchers are investigating the strong openness property and stability of multiplier submodule sheaves associated with singular Nakano semipositive Hermitian metrics.

Would you like more details on any of these topics? I can help break them down further!

参考Link（殆ど 下記 Abstract通り？）
https://link.springer.com/article/10.1134/S0040577924010112
Home Theoretical and Mathematical Physics Article
Recent progress in the theory of functions of several complex variables and complex geometry
Research Articles
Published: 01 February 2024
Volume 218, pages 163–176, (2024) Xiangyu Zhou
Cite this article
Abstract
We give a survey on recent progress on converses of L^2 existence theorem and L^2
extension theorem which are two main parts in
L^2 -theory, and their applications in getting criteria of Griffiths positivity and characterizations of Nakano positivity of (singular) Hermitian metrics of holomorphic vector bundles, as well as the strong openness property and stability property of multiplier submodule sheaves associated to singular Nakano semipositive Hermitian metrics on holomorphic vector bundles.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1724146576/958

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